Has to be Delta marketed - so requires it to be a codeshare
For Virgin Atlantic, Korean Air and Aeromexico, upgrades are only valid for Delta marketed flights. ... Valid on Delta-marketed, Korean Air-operated flights for use globally on Delta's published fares booked in Y or B class to Korean Air's Z class, or booked in M class to Korean Air's O class.
Even then note the fare class is very restricted and is basically full fare coach in order to upgrade. Its almost impossible to find O on KE, and Z is a little better but you'd need a Y or B fare so a discounted business ticket may actually cost less.